The Thermoviscous Acoustics, Transient (tatd) interface (), found under the Thermoviscous Acoustics branch () when adding a physics interface, is used to compute the transient evolution of the acoustic variations in pressure, velocity, and temperature. The interface is the time domain equivalent of The Thermoviscous Acoustics, Frequency Domain Interface. This physics interface is required to accurately model acoustics in geometries of small dimensions. Near walls, viscous losses and dissipation due to thermal conduction become important because boundary layers exists. The thicknesses of these boundary layers are known as the viscous and thermal penetration depth. For this reason, it is necessary to include thermal conduction effects and viscous losses explicitly in the governing equations. It is, for example, used when modeling the response of transducers like microphones, miniature loudspeakers and receivers. Other applications include analyzing feedback in hearing aids, smart phones and in mobile devices, or studying the damped vibrations of MEMS structures.

The physics interface solves the equations in the time domain. The model can be extended to model nonlinear effects by adding the Nonlinear Thermoviscous Acoustics Contributions feature. In the time domain it is also possible to model nonlinear effects due to topology changes, like nonlinear squeeze film damping. This is achieved when combining the interface with the Moving Mesh functionality.

The equations defined by the Thermoviscous Acoustics, Transient interface are the first and second order perturbation formulation of the Navier-Stokes equations in quiescent background conditions solving the continuity, momentum, and energy equations. Due to the detailed description necessary when modeling thermoviscous acoustics, the model simultaneously solves for the acoustic pressure p, the acoustic velocity variation u (particle velocity), and the acoustic temperature variations T. It is available for 3D, 2D, and 1D Cartesian geometries as well as for 2D and 1D axisymmetric geometries.

The Thermoviscous Acoustics, Transient interface is, as the frequency domain variant, formulated in the so-called scattered field formulation where the total field (subscript t) is the sum of the scattered field (the field solved for, p, u, and T) and a possible background acoustic field (subscript b), such that

The scattered field formulation is not applicable in domains where the Nonlinear Thermoviscous Acoustics Contributions are included. When no Background Acoustic Fields feature is present (the background field values are zero per default) the total field is simply the field solved for, pt = p, ut = u, and Tt = T. All governing equations and boundary conditions are formulated in the total field variables.

When this physics interface is added, these default nodes are also added to the Model Builder — Thermoviscous Acoustics Model, Wall, and Initial Values. Then, from the Physics toolbar, add other nodes that implement, for example, boundary conditions and sources. You can also right-click Thermoviscous Acoustics to select physics features from the context menu.

The Label is the default physics interface name.

The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.

The default Name (for the first physics interface in the model) is tatd.

Expand the Equation section to see the equations solved for with the Equation form specified. The default selection for Equation form is set to Study controlled. The available studies are selected under Show equations assuming.

See Thermoviscous Acoustics Equation Settings.

To display this section, click the Show More Options button () and select Stabilization. Select No stabilization applied (the default), Galerkin least-squares (GLS) stabilization, or Streamline upwind Petrov-Galerkin (SUPG) stabilization. When linear thermoviscous acoustic problems are solved, the problem is stable (with the default P1-P2-P2 discretization), but as soon as the Nonlinear Thermoviscous Acoustics Contributions feature is used, stabilization may be required. For weakly nonlinear problems no, stabilization is necessary, but for moderate and highly nonlinear problems using stabilization is essential. In most of those cases, use the Galerkin least-squares (GLS) stabilization option.

Enter the Maximum frequency to resolve in the model. The default frequency is set to 1000[Hz] but should be changed to reflect the frequency content of the sources used in the model. Select the Time stepping (method) as Fixed (preferred) the default and recommended or Free. The Free option is in general not recommended for wave problems. The generated solver will be adequate in most situations if the computational mesh also resolves the frequency content in the model. Note that any changes made to these settings (after the model is solved the first time) will only be reflected in the solver if Show Default Solver or Reset Solver to Defaults is selected in the study.

From the list select the element order and type (Lagrange or serendipity) for the Pressure, the Velocity field, and the Temperature variation, respectively. The default is Linear for the pressure and Quadratic Lagrange for the velocity and the temperature.

This physics interface defines these dependent variables (fields), the Pressure p, the Velocity field u and its components, and the Temperature variation T. The names can be changed but the names of fields and dependent variables must be unique within a model.